There are many tens of billions of investment in prerequisites such as getting rid of level crossings and properly secure rail and upgrading stations and trains that'd be required before you can even think of upgrading mainline rail to driverless. For the London Underground, it means a rolling program of platform upgrades, signalling upgrades and rolling stock upgrades that'd similarly be in the many billions.
And yes, now would be the right time to finance it, but even if you start now this is just not happening in the next couple of decades, that was my point.
So by all means, it's worth starting to make the pre-requisite improvements, but it won't bring driverless trains on most of these lines anytime soon.
If we can fly drones through the deserts of Arabia why can't we drive trains remotely through the suburbs of Croydon?
It's if anything one of the worst places in the entire UK to start such a project.
The problem with what you suggest is that a ten minutes delay at East Croydon during rush hour, if you're lucky and a problem happens near a station, can easily lead to rush hour traffic from large parts of the South Coast to both London Victoria and London Bridge piling up with effects lasting for an hour or more. It's a horrible chokepoint. There are plans to fix that [1], but those plans also involve multi-year projects. In fact the planning has been going on for years at this point.
A similar issue is a problem for the London Underground - while there are fewer complex junctions, the margins are far tighter. A train that's stuck on the station for a couple of minutes can have knock on effects over a larger area.
All of this is solvable, but the costs involved in various improvements to mitigate them means it'd take a very long time before those investments would start paying off.
[1] https://www.networkrail.co.uk/running-the-railway/our-routes...
And yes, it does fail. Been on trains when the doors refused to open because the system failed to recognise the station. For ages, the trains also waited for ~30 seconds to open doors at London Victoria, supposedly because the system that recognised the stations used GPS, and the station concourse at Victoria is too deep for the trains to get a signal. Don't know if that is true or not, but in any case automating even door control was a long, complex project that still has issues years later.
Steps will keep being taken towards automating more of it, but there is decades old rolling stock, so any upgrades will take accordingly long to spread through the system as everything gets upgraded.
Isle of Wight for example, ran on London Underground 1938 stock trains until last year, when they started upgrading to refurbished British Rail Class 484 rolling stock built in the 1970's and 1980's...
With respect to renewables, not all of the UK network is even electrified yet...